I am worried that a bill will fall through the cracks and one of my units will have their water turned off or a faulty floorboard will go unfixed for months or something similar.What systems do you use to track expenses and "status" of each unit?

What if your tenant has a great credit score but looks at their pet as property- keeps it outside, unfixed & never sees the vet?

You need to hire a lawyer, go in front of the judge, explain what you want to do ..and then city inspector says: nope ..the property requires $X to be fixed ..unfixable ..needs to be demoed..then what ?

Water, dirt, and other substances can now get in and under that tile because it became unfixed from the floor. 

I just replaced mine, two weeks to determine old one was unfixable,  had to wait an extra week for delivery because model with rebate was out of stock.  

If watching the grass die and the window screens disappear while they sneak in an unfixed that urinates & sprays all over the place doesn't bother you, go for it.  

Good idea to leave a few things unfixed, in fact sometimes we actually leave some minor things (non-safety related) just to see if an inspector will catch them.

WE have seen mold, leaks and other issues that needed immediate attention but went unfixed for months because the resident never reported it to us. 

What happens if the seller agrees to fix everything important but leaves one unfixed?

Look under sinks for water damage unfixed or painted over.